795 citations · 1.3k across the 32 of their papers we have counts for
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Implicit regularization in AI meets generalized hardness of approximation in optimization -- Sharp results for diagonal linear networks
Johan S. Wind, Vegard Antun, Anders C. Hansen
Understanding the implicit regularization imposed by neural network architectures and gradient based optimization methods is a key challenge in deep learning and AI. In this work w…
The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networks
Alexander Bastounis, Anders C Hansen, Verner Vlačić
The unprecedented success of deep learning (DL) makes it unchallenged when it comes to classification problems. However, it is well established that the current DL methodology prod…
Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem
Matthew J. Colbrook, Vegard Antun, Anders C. Hansen
Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when…
The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems
Nina M. Gottschling, Vegard Antun, Anders C. Hansen +1
Methods inspired by Artificial Intelligence (AI) are starting to fundamentally change computational science and engineering through breakthrough performances on challenging problem…